On the complexity of the steepest-descent
with exact linesearches
C. Cartis, N. I. M. Gould and Ph. L. Toint
NAXYS-16-2012 September 2012
The worst-case complexity of the steepest-descent algorithm with exact
linesearches for unconstrained smooth optimization is analyzed, and it is shown
that the number of iterations of this algorithm which may be necessary to find
an iterate at which the norm of the objective function's gradient is less that
a prescribed $\epsilon$ is, essentially, a multiple of $1/\epsilon^2$, as is
the case for variants of the same algorithms using inexact linesearches.